Vlasov方程的精确解

该文将等熵磁流体力学（ＭＨＤ）或等熵电磁流体力学（ＥＭＨＤ）的基本方程组以及（非相对论的或相对论的）Ｖｌａｓｏｖ方程，分别化为等熵流体力学（ＨＤ）表象，建立了上述三类等熵方程之间的对应关系．从而使非相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＭＨＤ方程的精确解相对应）和相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＥＭＨＤ方程的精确解相对应）都可以用（非相对论的和相对论的）等熵ＨＤ方程的精确解来表示．     

ODE方程精确解及其应用

本文得到了一类ＯＤＥ方程精确解,并给出了它在Ｃｈａｆｆａ－Ｉｎｆａｎｔｅ方程和波方程上的应用。     

解线性抛物方程的一类新格式

解线性抛物方程的一类新格式孙志忠（中国科学院计算中心）ＡＮＥＷＣＬＡＳＳＯＦＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＦＯＲＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＳｕｎＺｈｉ－ｚｈｏｎｇ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，Ａ...     

解拟线性抛物方程的一类二阶差分格式

解拟线性抛物方程的一类二阶差分格式孙志忠（中国科学院计算中心）ＡＣＬＡＳＳＯＦＳＥＣＯＮＤ－ＯＲＤＥＲＡＣＣＵＲＡＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＦＯＲＱＵＡＳＩ－ＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＳｕｎＺｈｉ－ｚｈｏｎｇ（Ｃｏ...     

n维Reyleigh方程周期解的存在性

本文主要讨论ｎ维Ｒａｙｌｅｉｇｈ方程周期解的存在性。利用Ｍａｗｈｉｎ的重合度理论，我们给出了周期解存在的两个充分条件。对其特例ｎ维Ｄｕｆｆｉｎｇ方程给出了周期解存在唯一的条件。     

Yang-Baxter方程的解与量子Yang-Baxter H-余模

设Ｈ是域ｋ上的Ｈｏｐｆ代数。本文首先讨论了量子Ｙａｎｇ－Ｂａｘｔｅｒ Ｈ－余模与Ｙａｎｇ－Ｂａｘｔｅｒ方程的解的关系;然后作为应用,给出了任意Ｈｏｐｆ代数上Ｙａｎｇ－Ｂａｘｔｅｒ方程的一个解。     

四阶Ginzburg-Landau型方程的初值问题

本文研究四阶Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ型方程的初值问题,通过建立一般半线性抛物方程的Ｌτ－解和Ｈｓ－解之间的联系,获得该方程的整体Ｈｓ－解的存在唯一性(ｓ＝１、２)。     

四元数分析中的T算子与两类边值问题

本文研究四元数分析中的非齐次 Ｄｉｒａｃ方程．引入了这类方程的分布解即 Ｔ算子,证明了Ｔ算子的一些性质并考察了非齐次Ｄｉｒａｃ方程的Ｄｉｒｉｃｈｌｅｔ边值问题,并将结果推广到高阶非齐次Ｄｉｒａｃ方程及这种方程的一类边值问题的情况．     

一类非线性电报方程的多重周期解

本文讨论一类非线性电报方程的周期－Ｄｉｒｉｃｈｌｅｔ边值问题解的多重性，在非线性项满足一定渐近线性条件的情况下，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ度数理论得到了一个关于此类电报方程的多解定理。     

耗散KDV型方程Cauchy问题的整体吸引子

该文对耗散ＫＤＶ型方程的动力学行为进行了讨论,得到了该方程在Ｈ＾２（Ｒ＾１）上存在整体吸引子。     

定态耦合Harry-Dym方程的Bargmann坐标及约束系统的Poisson结构

该文首先给出相联于耦合Harry-Dym(CHD)族的Lenard递归方程的多项式解,并证明了任一定态CHD方程的解均有可积的Bargmann坐标表示.最后讨论了约束系统的动力r-矩阵及Poisson结构.     

A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line

In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem.     

Multiparameter spectral problem for some weakly coupled systems of Hamiltonian equations

We consider a multiparameter spectral problem for a weakly coupled system of ordinary differential equations in which every equation is Hamiltonian and contains two unknown functions. Using the notion of the number of an eigenvalue for a problem with one such equation, we give a statement of the problem of finding the desired eigentuple of values for the problem with several equations. We prove the existence and uniqueness of a solution of this problem and suggest and study a numerical solution method.     

On bounded solutions of transport equation solved with a spectral method

In this article, a spectral method accompanied by finite difference method has been proposed for solving a boundary value problem that accompanies a stationary transport equation. We also prove that the solution is bounded by a value that depends of the source function. The accuracy and computational efficiency of the proposed method are verified with the help of a numerical example. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012     

Inverse problem for an equation of parabolic-hyperbolic type with a nonlocal boundary condition

For an equation of the parabolic-hyperbolic type, we consider an inverse problem with a nonlocal condition relating solution derivatives that belong to different types of the equation in question. We justify a uniqueness criterion and prove the existence of a solution of the problem by the spectral analysis method. We prove the stability of the solution with respect to the nonlocal boundary condition.     

On the stability and the attraction domain of the stationary solution of a singularly perturbed parabolic equation with a multiple root of the degenerate equation

We construct and justify the asymptotics of a boundary layer solution of a boundary value problem for a singularly perturbed second-order ordinary differential equation for the case in which the degenerate (finite) equation has an identically double root. A specific feature of the asymptotics is the presence of a three-zone boundary layer. The solution of the boundary value problem is a stationary solution of the corresponding parabolic equation. We prove the asymptotic stability of this solution and find its attraction domain.     

Two-dimensional rotating waves in a functional-differential diffusion equation with rotation of spatial arguments and time delay

We consider the Neumann boundary value problem for a parabolic functional-differential equation in a disk. We describe spatially inhomogeneous solutions in the form of rotating waves branching from the homogeneous stationary solution in the case of an Andronov-Hopf bifurcation. By passing to a moving coordinate system and by reducing the original problem to a stationary boundary value problem for a partial differential equation with a deviating argument, we prove the existence of rotating waves appearing in the disk under the Andronov-Hopf bifurcation.     

Two-Dimensional Navier-Stokes Equations Driven by a Space-Time White Noise

We study the two-dimensional Navier-Stokes equations with periodic boundary conditions perturbed by a space-time white noise. It is shown that, although the solution is not expected to be smooth, the nonlinear term can be defined without changing the equation. We first construct a stationary martingale solution.Then, we prove that, for almost every initial data with respect to a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense.     

Akustische wellen in Gebieten,die von zwei lokal gestorten parallelen ebenen begrenzt sind

We consider acoustic waves in domains with boundaries, coinciding with two parallel planes outside a sufficiently large sphere. Several results on spectral properties of the Laplace operator in such domains are derived and used to prove uniqueness and existence of a solution of the Dirichlet boundary value problem for the reduced wave equation under additional restrictions. In particular, a class of domains is described for which no eigenvalues are present.     

Analysis of an elliptic-parabolic free boundary problem modelling the growth of non-necrotic tumor cord

We study a free boundary problem modelling the growth of a tumor cord in which tumor cells live around and receive nutrient from a central blood vessel. The evolution of the tumor cord surface is governed by Darcy's law together with a surface tension equation. The concentration of nutrient in the tumor cord satisfies a reaction-diffusion equation. In this paper we first establish a well-posedness result for this free boundary problem in some Sobolev-Besov spaces with low regularity by using the analytic semigroup theory. We next study asymptotic stability of the unique radially symmetric stationary solution. By making delicate spectrum analysis for the linearized problem, we prove that this stationary solution is locally asymptotically stable provided that the constant c representing the ratio between the diffusion time of nutrient and the birth time of new cells is sufficiently small.